There's a bunch of replies here that are going to cost you a lot money .
Start with the question in general , motor starting varies a lot , but a general rule of thumb is a min. of 2-3 times the running current .
I going to use approximate , but even numbers , that are close to make the points .
So you have an AC unit that takes 500 watts to run , and min. 1,000 watts to start - what about some conditions varying and now you need 3,000 watts ?
You also have to watch out for the bs from the sales people , keep the idea of margins in mind when estimating anything .
So you buy a generator labeled 2,000 watts [ being older and having been in the repair bis , the large numbers used to be honest - the running current / now the large number , at best are the surge ] so your new generator - if you read the documentation that came with it says starting current is 1,600 watts .
Average price of that generator is over $1,000 + plus the labor to replace ? , average price of your AC $900 , so an average of close to $2,500 .
HOW OFTEN DO YOU WANT TO SPEND THAT MONEY , OVER & OVER AGAIN ?
The 1st two replies on Googling RV AV starting watts -
https://www.google.com/search?q=rv+...j69i57j0l4.14855j0j7&sourceid=chrome&ie=UTF-8
So a 8,000 btu starts with 1,850 watts , with a 2,000 watt generator .
Or 10,000 btu takes 2,00 and start with 2,000 with same generator .
Or 13,500 btu 2,800 starting watts and start with same 2,000 generator . " no problems " ?!
So you drive your car like a race car , or you drive your RV like a semi-truck - how long do you think either is going to last .
Now if those abusing there equipment would tell you the truth after what a season , more or less , that they killed both the generator & AC , they may not die at the same time but both will have a short life .
Ask anybody in the repair bis. , that is not trying to sell you something and is honest .
So do not anticipate the best conditions & send the lest on the cheapest .
Engineering principles do something like anticipate the worst conditions , so at least 3 times starting current , not 2 times .
Then you get many benefits your equipment will last longer , run better , run cheaper [ generators get better gas millage if the cruising - peak power point ] on something like the Honda , look at the spec. sheet for consumption 3 gal per hr max , 8 gal per hr 1/4 load , so a real load for long life is 1/2 load = 800 watts .
Lastly , most AC systems nowdays , use a thermostat , this means that the AC unit compressor shuts down frequently , once the set point is reached / and then startup again , now how often do you run your AC in the summer , many times 24 hrs. a day .